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Question:
I am having a hard time trying to figure out how to raise the imaginary unit i to the imaginary power i. In other words: i^i = ? Where can I find more information on complex forms of Ln?



Replies:
Raising complex numbers to powers is often simplified by using Euler's
Formula:
exp(i*x) = cos(x) +i*sin(x) You see for example, that for x=pi this becomes exp(i*pi) = -1 since sin(pi)=0.

Similarly, exp(i * pi/2) = i, since cos(pi/2) = 0 and sin(pi/2) = 1

So i^i = [exp(i*pi/2)]^i = exp(i^2 *pi/2) = exp(-1*pi/2) = 0.207879...

WHICH IS REAL! AMAZING these complex numbers!

I think you will have to consult a textbook on complex variables to get detailed info on log functions of complex numbers, and of trig functions.

Vince Calder



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